A first model-independent radial BAO constraint from the final BOSS sample

Using almost one million galaxies from the final Data Release 12 of the SDSS's Baryon Oscillation Spectroscopic Survey, we have obtained, albeit with low significance, a first model-independent determination of the radial BAO peak with 9% error: $\Delta z_{\rm BAO}(z_{\rm eff}=0.51)= 0.0456 \pm 0.0042$. In order to obtain this measurement, the radial correlation function was computed in 7,700 angular pixels, from which mean correlation function and covariance matrix were obtained, making the analysis completely model independent. This novel method of obtaining the covariance matrix was validated via the comparison with 500 BOSS mock catalogs. This $\Delta z_{\rm BAO}$ determination can be used to constrain the background expansion of exotic models for which the assumptions adopted in the standard analysis cannot be satisfied. Future galaxy catalogs from J-PAS, DESI and Euclid are expected to significantly increase the quality and significance of model-independent determinations of the BAO peak, possibly determined at various redshift and angular positions. We stress that it is imperative to test the standard paradigm in a model-independent way in order to test its foundations, maximize the extraction of information from the data, and look for clues regarding the poorly understood dark energy and dark matter.